Two effective theories (EFTs) have come to the fore in trying to extend the successful Standard Model in the ignorance of which new physics may be present at a higher energy (if there is any).
There are many aspects of the Standard Model that can be pursued at accelerators (the many-parameter flavor structure in both lepton and quark sectors, the Higgs couplings to the fermions, the CP violating phases, QCD processes...) but at the energy frontier the most important aspects of physics that is being clarified right now is the nature of the mechanism of Electroweak (EW) Symmetry Breaking: whether it happens as the well-known discussion in the Standard Model paradigm, or whether new particles or interactions influence the global \(SU(2)\times SU(2)\rightarrow SU(2)\)  breaking pattern that is at the crux of electroweak interactions.
Several extended works have dealt with many of these aspects, for example [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
